A stable set of primes of the form j^2 + k^2 with all j and k distinct.
13, 17, 89, 149, 157, 313, 337, 421, 613, 929, 937, 1117, 1213, 1409, 1861, 1997, 2113, 2521, 2969, 3457, 3469, 3613, 4513, 4517, 5309, 5737, 5953, 6037, 6397, 6869, 7333, 8089, 8849, 9497, 9661, 9721, 10513, 12037, 12329, 12437, 12973, 13297, 14969, 15373
1
The sequence S000616 lists the pairs (j,k) for each number here. This sequence is discussed in the Greenfield and Greenfield paper. The fourth-power is shown in S000617.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
L. E. Greenfield and S. J. Greenfield, Some Problems of Combinatorial Number Theory Related to Bertrand's Postulate, J. Integer Sequences, 1998, #98.1.2.
(Mma) n = 200; lst = Reverse[Range[2 n]]; prms = {}; Do[m = lst[[1]]; lst = Delete[lst, 1]; pos = 1; While[p = m^2 + lst[[pos]]^2; Not[PrimeQ[p]], pos++]; AppendTo[prms, p]; lst = Delete[lst, pos], {i, n}]; Take[Sort[prms], n/2]
Cf. A091652, S000616, S000617.
nonn
T. D. Noe, May 05 2015